Expression of type ExprTuple

from the theory of proveit.linear_algebra.vector_sets

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, K, Lambda, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets, VecSpaces
from proveit.logic import And, Equals, Forall, InSet, NotInSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(sub_expr1, Bases(V)), And(InSet(sub_expr1, SpanningSets(V)), NotInSet(sub_expr1, LinDepSets(V))).with_wrapping_at(2)).with_wrapping_at(2), domain = V).with_wrapping(), domain = NaturalPos), domain = VecSpaces(K))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\right)\right) =  \\ \left(\begin{array}{c} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{SpanningSets}\left(V\right)\right) \land  \\ \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \notin \textrm{LinDepSets}\left(V\right)\right) \end{array}\right) \end{array} \end{array}\right)\end{array}\right]\right]\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 19 body: 2
2	Operation	operator: 20 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 57 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 20 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	57, 12
11	Lambda	parameter: 60 body: 14
12	Operation	operator: 15 operand: 19
13	ExprTuple	60
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operand: 23
18	Operation	operator: 46 operands: 22
19	Variable
20	Literal
21	ExprTuple	23
22	ExprTuple	60, 24
23	Lambda	parameters: 53 body: 25
24	Literal
25	Conditional	value: 26 condition: 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 35 operands: 30
28	Literal
29	ExprTuple	31, 32
30	ExprTuple	33
31	Operation	operator: 46 operands: 34
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 59 end_index: 60
34	ExprTuple	49, 38
35	Literal
36	ExprTuple	39, 40
37	Lambda	parameter: 64 body: 41
38	Operation	operator: 42 operand: 57
39	Operation	operator: 46 operands: 43
40	Operation	operator: 44 operands: 45
41	Operation	operator: 46 operands: 47
42	Literal
43	ExprTuple	49, 48
44	Literal
45	ExprTuple	49, 50
46	Literal
47	ExprTuple	61, 57
48	Operation	operator: 51 operand: 57
49	Operation	operator: 52 operands: 53
50	Operation	operator: 54 operand: 57
51	Literal
52	Literal
53	ExprTuple	56
54	Literal
55	ExprTuple	57
56	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
57	Variable
58	Lambda	parameter: 64 body: 61
59	Literal
60	Variable
61	IndexedVar	variable: 62 index: 64
62	Variable
63	ExprTuple	64
64	Variable